Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



An optimum implicit recurrence formula for the heat conduction equation

Author: Stephen H. Crandall
Journal: Quart. Appl. Math. 13 (1955), 318-320
MSC: Primary 65.0X
DOI: https://doi.org/10.1090/qam/73292
MathSciNet review: 73292
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  • [1] E. Schmidt, Über die Andwendung der Differenzenrechnung auf technische Anheiz-und-Abkühungsprobleme, A. Föppl Festschrift, Springer, Berlin, 1924, pp. 179-189
  • [2] J. Crank and P. Nicolson, A practical method for numerical evaluation of solutions of partial differential equations of heat-conduction type, Proc. Camb. Phil. Soc. 32, 50-67 (1947) MR 0019410
  • [3] G. G. O'Brien, M. A. Hyman and S. Kaplan, A study of the numerical solution of partial differential equations, J. Math. Phys. 29, 223-251 (1951) MR 0040805
  • [4] W. E. Milne, Numerical solution of differential equations, John Wiley, N. Y., 1953, p. 122 MR 0068321
  • [5] C. M. Fowler, Analysis of numerical solutions of transient heat-flow problems, Quart. Appl. Math. 3, 361-376 (1946) MR 0015190
  • [6] S. H. Crandall, Implicit vs. explicit recurrence formulas for the linear diffusion equation. J. Assoc. Comput. Mach. 2, 42-49 (1955) MR 0068911
  • [7] See, for example, F. B. Hildebrand, Methods of applied mathematics, Prentice-Hall, N. Y., 1952, p. 330
  • [8] For six possible alternatives see P. H. Price and M. R. Slack, Stability and accuracy of numerical solutions of the heat flow equation, Brit. J. Appl. Phys. 3, 379-384 (1952)

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DOI: https://doi.org/10.1090/qam/73292
Article copyright: © Copyright 1955 American Mathematical Society

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